Compliance testing of two or more water quality determinands using quantiles

Abstract

AbstractThe testing of k > 1 water quality determinands for compliance with environmental regulations leads to difficulties in finding the probabilities of wrongly concluding (a) that one or more determinands failed when in fact all passed (joint type I error), and (b) that one or more passed when all failed (joint type II error). Also, owing to dependence among the determinands, some may contribute little to the compliance assessment and, if they serve no other purpose, are a waste of analytical resources. A method based on sample quantiles is suggested for estimating the theoretical number f of completely independent, notional determinands whose information content is equivalent to the k actual determinands being regulated. Next, the alternative strategies of individual and collective testing of the k determinands against regulations set as quantiles are compared in terms of joint type I and II error probabilities. The extreme cases of negative and positive dependence among the determinands set ranges for these probabilities, but even with moderate k they tend to be impractically broad for reliable decision making with either test strategy. Assuming independence as a worst case instead of negative dependence helps somewhat. It is explained how, alternatively, point estimates for the error probabilities are possible using f, given certain assumptions. Two schemes for regulating multiple determinands thus emerge, one based on an agreed worst‐case situation which places minimal reliance on assumed conditions, the other based on an estimated error situation utilizing f. The choice between them would be influenced by the rigour required of the tests. The relative performance of individual and collective testing is shown to depend on the parameters chosen for the tests, and the degree and sign of dependence among the determinands. The design of compliance testing schemes is crucial in determining whether most risk lies with waste producers or the receiving environment, and what effect the prescribed regulations will actually have in practice.